Method of monitoring brain function

ABSTRACT

A method for assessing brain state by analysing mammalian brain electroencephalogram (“EEG”) recordings using an eighth order autoregressive and fifth order moving average discrete time equation.

FIELD OF THE INVENTION

The present invention relates to a method and system for the applicationof a mathematical model, and in particular a fixed order auto-regressivemoving average model, to analyse electroencephalogram (“EEG”) signalsgenerated by a subject in order to assess and monitor the subject'sbrain function under conditions of health, disease and therapeuticintervention.

BACKGROUND OF THE INVENTION

In clinical practice involving alterations in the level ofconsciousness, such as during the administration of sedatives or generalanaesthetic agents, it is important to be able to quantify brainfunction. Most approaches rely upon the analysis of the brain's surfaceelectrical activity, known as the electroencephalogram or EEG. Ingeneral the signal analysis method chosen is based on the statisticalproperties of the signal being analysed. The more closely matched themethod used is to the signal properties, the more reliable, meaningfuland accurate the resulting analysis will be. However these signalproperties can only be known if the mechanisms and processes responsiblefor the generation of the signal are also known.

To date none of these analysis methods of the brain's rhythmicelectrical activity have incorporated any details of the underlyingphysiological mechanisms responsible for its genesis. Therefore theirability to measure, and thus monitor, brain function in the clinicalsetting is limited.

This problem is overcome by the present invention which provides a morerational means of assessing and measuring brain function based on thedetailed knowledge of the physiological mechanisms underlying thegeneration of the brain's surface rhythmic electrical activity.

The theory underlying the present invention considers the cortex of thebrain as a single excitable spatial continuum of reciprocally connectedexcitatory and inhibitory neurons interacting by way of short-ranged(intra-cortical) and long-range (cortico-cortical) connections. As such,the brain is seen as a dynamically evolving entity rather than asynthetic processing unit like a computer.

Based on this theory, the characteristics of alpha rhythms arising as aconsequence of the brain's neural connections can be closely representedby a mathematical model, and in particular, a fixed orderauto-regressive moving average (“ARMA”) model. The present inventionderives specific values for the moving average (“MA”) andauto-regressive (“AR”) orders for the ARMA model based on theelectrocortical transfer function. The electrocortical transfer functiondescribes in a mathematical form the origin of the EEG readings taken ofa subject.

By applying EEG signals recorded from a subject to the fixed order ARMAmodel, coefficients can be obtained. To understand how thesecoefficients can be used to measure brain function, the equationsdefining the fixed order ARMA model are rewritten in the z-domain(complex domain) and are solved to obtain complex number solutions(called “poles”) that are mapped onto the z-plane. These poles representthe state of the brain at the specific point in time when the EEG signalwas recorded. Variations in the EEG signal, such as that induced byapplying sedatives to the subject, can be detected as variations of themean location of one or more poles on the z-plane. These variations canbe interpreted to measure brain function or to indicate changes in thestate of the brain.

By using the brain assessment techniques of the invention, it ispossible to monitor the state of a subject in various circumstances. Forinstance, the method of the invention can be used to monitor thevigilance or alertness of a subject when performing certain tasks suchas driving vehicles of various types or controlling critical equipment.In applications of this type, the method can be applied locally so as towarn the driver or controller of a condition which is indicative of aloss of vigilance or alertness so that appropriate action can be taken.The monitoring could be carried out remotely as well as locally.

The method of the invention can be used to monitor a subject whilstsleeping so as to assess various stages in sleep of a subject. Theresults obtained can be used for determination and/or treatment ofsleeping disorders.

Further, the invention can be used to monitor the state of anaesthesiaof a patient. In this application it would be typical for theanaesthetist (or an operator) to obtain a display of poles in the saidplane prior to administration of the anaesthetic. The method of theinvention can then be continued after application of the anaesthetic sothat the state of anaesthesia of the patient can be monitored as afunction of time by reference to the movement of clusters of polesdisplayed on display equipment. This provides useful information to theanaesthetist regarding the state of anaesthesia of the subject.

SUMMARY OF THE INVENTION

According to the present invention there is provided a method forassessing brain state by analysing human electroencephalographicrecordings using an eighth order autoregressive (“AR”) and fifth ordermoving average (“MA”) discrete time model based on a theory of theunderlying mechanism of generation of mammalian EEG activity.

The invention also provides a method for assessing brain state byanalysing human electroencephalographic recordings using an eighth orderautoregressive and fifth order moving average discrete time equation,taking a z-transform for said equations to obtain a z-domain equation,determining poles and zeroes in the solution of the z-domain equationand plotting the poles onto the complex plane.

The invention also provides a method of assessing the state of amammalian brain including the steps of:

(i) obtaining an electroencephalogram (EEG) from the brain;

(ii) digitising the EEG to define a digitised EEG data signal;

(iii) segmenting the EEG data signal into time frames of fixed length,y[n];

(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅;

(vi) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(vii) substituting each of the values of the coefficients into thez-domain equation;

(viii) solving A(z)=0 for z in the second equation to determine thepoles;

(ix) plotting the poles in the complex plane;

(x) repeating steps (iv) to (ix) for each frame in the sample todetermine clusters of poles in the complex plane; and

(xi) assessing the state of the brain by reference to the position anddistribution of at least some of said clusters of poles as mapped in thecomplex plane.

According to the present invention there is also provided a method ofassessing the state of a mammalian brain including the steps of:

(i) obtaining an electroencephalogram (EEG) from the brain;

(ii) digitising the EEG to define a digitised EEG data signal;

(iii) segmenting the EEG data signal into time frames of fixed length,y[n];

(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅;

(vi) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(vii) substituting each of the values of the coefficients into thez-domain equation;

(viii) solving A(z)=0 for z in the second equation to determine thepoles;

(ix) plotting the poles in the complex plane;

(x) repeating steps (iv) to (ix) for each frame in the sample todetermine clusters of poles in the complex plane;

(xi) administering an intervention to the brain;

(xii) repeating steps (i) to (x) at least once;

(xiii) monitoring movement of at least some of said clusters of poles inthe complex plane; and

(xiv) assessing the state of the brain by reference to movement of atleast some of said clusters of poles as mapped in the complex plane.

According to the present invention there is also provided a method ofassessing the state of a mammalian brain including the steps of:

(i) obtaining a first electroencephalogram (EEG) from the brain;

(ii) digitising the EEG to define a digitised EEG data signal;

(iii) segmenting the EEG data signal into time frames of fixed length,y[n];

(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅;

(vi) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(vii) substituting each of the values of the coefficients into thez-domain equation;

(viii) solving A(z)=0 for z in the second equation to determine thepoles;

(ix) plotting the poles in the complex plane;

(x) repeating steps (iv) to (ix) for each frame in the sample todetermine clusters of poles in the complex plane;

(xi) obtaining a second EEG from said brain at a later time;

(xii) repeating steps (ii) to (x) in relation to the second EEG at leastonce;

(xiii) monitoring the movement of at least some corresponding clustersof poles in the complex plane derived from the first and second EEGsrespectively; and

(xiv) assessing the state of the brain by reference to movement of atleast some of said clusters of poles as mapped in the complex plane.

For the methods above, an EEG may be obtained and recorded before it isprocessed. The recorded EEG can therefore be processed at any time afterit has been recorded or it can be used as a reference for comparisonswith other EEGs at a future point in time. Alternatively, an EEG may beobtained and processed on-the-fly such that an EEG is repeatedlyobtained over consecutive and constant time intervals, and where eachtime interval may overlap with the immediately preceding time interval.The EEG obtained for each time interval is immediately processed by themethods described above.

Preferably, step (x) is repeated up to 100 times so that there are aplurality of poles in each of the said clusters. Also step (x) may berepeated continuously to track the motion of the poles from eachsegment.

Preferably further, the method includes a step of taking the centroid ofthe poles for each cluster of poles, and monitoring and comparing themovement of the centroids.

The present invention further provides a system for performing the abovemethods. The present invention further provides computer readable mediahaving computer program instructions stored thereon which, when executedby a computer, perform the methods described above.

The invention also provides a method of assessing the efficacy of acognitively active pharmaceutical agent including the steps of:

(i) obtaining a first electroencephalogram (EEG) from the brain of asubject;

(ii) digitising the EEG to define a digitised EEG data signal;

(iii) segmenting the EEG data signal into time frames of fixed length,y[n];

(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅;

(vi) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(vii) substituting each of the values of the coefficients into thez-domain equation;

(viii) solving A(z)=0 for z in the second equation to determine thepoles;

(ix) plotting the poles in the complex plane;

(x) repeating steps (iv) to (ix) for each frame in the sample todetermine clusters of poles in the complex plane;

(xi) administering a dose of a cognitively active pharmaceutical agentto the subject;

(xii) obtaining a second EEG from said brain after step (xi);

(xiii) repeating steps (ii) to (x) in relation to the second EEG atleast once;

(xiv) monitoring the movement of at least some corresponding clusters ofpoles in the complex plane derived from the first and second EEGsrespectively; and

(xv) assessing the efficacy of the cognitively active pharmaceuticalagent by reference to movement of at least some of said clusters ofpoles as mapped in the complex plane.

The invention also provides a method of assessing the state of vigilanceor alertness of a subject including the steps of:

(i) obtaining an electroencephalogram (EEG) from the brain of a subject;

(ii) digitising the EEG to define a digitised EEG data signal;

(iii) segmenting the EEG data signal into time frames of fixed length,y[n];

(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅;

(vi) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(vii) substituting each of the values of the coefficients into thez-domain equation;

(viii) solving A(z)=0 for z in the second equation to determine thepoles;

(ix) plotting the poles in the complex plane;

(x) repeating steps (iv) to (ix) for each frame in the sample todetermine clusters of poles in the complex plane;

(xi) repeating steps (i) to (x);

(xii) monitoring movement of at least some of said clusters of poles inthe complex plane; and

(xiii) assessing the state of vigilance or alertness of the subject byreference to movement of at least some of said clusters of poles asmapped in the complex plane.

The invention also provides a method of assessing the state of sleep ofa subject including the steps of:

(i) obtaining an electroencephalogram (EEG) from the brain of a subject;

(ii) digitising the EEG to define a digitised EEG data signal;

(iii) segmenting the EEG data signal into time frames of fixed length,y[n]; (iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅;

(vi) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(vii) substituting each of the values of the coefficients into thez-domain equation;

(viii) solving A(z)=0 for z in the second equation to determine thepoles;

(ix) plotting the poles in the complex plane;

(x) repeating steps (iv) to (ix) for each frame in the sample todetermine clusters of poles in the complex plane;

(xi) repeating steps (i) to (x);

(xii) monitoring movement of at least some of said clusters of poles inthe complex plane; and

(xiii) assessing the state of sleep of the subject by reference tomovement of at least some of said clusters of poles as mapped in thecomplex plane.

The invention also provides a method of assessing the state ofanaesthesia of a subject including the steps of:

(i) obtaining an electroencephalogram (EEG) from the brain of a subjectwhile anaesthetised;

(ii) digitising the EEG to define a digitised EEG data signal;

(iii) segmenting the EEG data signal into time frames of fixed length,y[n];

(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅;

(vi) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(vii) substituting each of the values of the coefficients into thez-domain equation;

(viii) solving A(z)=0 for z in the second equation to determine thepoles;

(ix) plotting the poles in the complex plane;

(x) repeating steps (iv) to (ix) for each frame in the sample todetermine clusters of poles in the complex plane;

(xi) repeating steps (i) to (x);

(xii) monitoring movement of at least some of said clusters of poles inthe complex plane; and

(xiii) assessing the state of anaesthesia of the subject by reference tomovement of at least some of said clusters of poles as mapped in thecomplex plane.

The invention also provides apparatus for assessing brain state of asubject, the apparatus including a plurality of electrodes for pickingup EEG signals from the brain of the subject;

digitising means for converting the EEG signals to a digitised EEG datasignal;

computing means for:

(i) segmenting the EEG data signal into time frames of fixed length,y[n];

(ii) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$

(iii) solving the first equation to determine coefficients a₁ to a₈ andb₀ to b₅;

(iv) performing a z-transform on the first equation to obtain a second,z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$

(v) substituting each of the values of the coefficients into thez-domain equation;

(vi) solving A(z)=0 for z in the second equation to determine the poles;

(vii) plotting the poles in the complex plane; and

display means for displaying the poles, to thereby enable assessment ofthe brain state of the subject by reference to the position anddistribution of clusters of said poles.

BRIEF DESCRIPTION OF THE DRAWINGS

Preferred embodiments of the present invention are hereinafterdescribed, by way of example only, with reference to the accompanyingdrawings, wherein:

FIG. 1 is a schematic diagram showing one example of the apparatus ofthe invention;

FIG. 2 is a diagram showing an example of the 8 poles derived from onesegment of an EEG signal plotted onto the z-plane;

FIG. 3 is a diagram showing an example of the cumulative positions ofthe 8 poles derived from several segments of an EEG signal plotted ontothe same z-plane.

FIG. 4 is a diagram showing the schematic representation on the z-planeof the predicted effects of increasing the strength of neuronalpopulation inhibitory→inhibitory and inhibitory→excitatory synapticinteractions;

FIG. 5 is a diagram showing the schematic representation on the s-plane(which can also be referred to as the Laplace or Fourier plane) of thepredicted effects of increasing the strength of neuronal populationinhibitory→inhibitory and inhibitory→excitatory synaptic interactions;

FIG. 6 is an example of the upper right quadrant of the z-plane in apole-zero plot for a typical subject before (as shown by the “−BZ” polesand zeros) and after (as shown by the “+BZ” poles and zeros) theadministration of the benzodiazepine, alprozolam, on the subject;

FIG. 7 is an example of a detailed view of a region of the upper rightquadrant of the z-plane between 8 to 13 Hz of a pole-zero plot for atypical subject before (as shown by the “−BZ” poles and zeros) and after(as shown by the “+BZ” poles and zeros) the administration of thebenzodiazepine, alprozolam, on the subject.

FIG. 8 is an example of the upper right quadrant of the z-plane in apole-zero plot for a typical subject before (as shown by the “−PL” polesand zeros) and after (as shown by the “+PL” poles and zeros) theadministration of a placebo on the subject;

FIG. 9 is an example of a detailed view of a region of the upper rightquadrant of the z-plane between 8 to 13 Hz of a pole-zero plot for atypical subject before (as shown by the “−PL” poles and zeros) and after(as shown by the “+PL” poles and zeros) the administration of a placeboon the subject;

FIG. 10 is an example of an EEG signal typically recorded from a subjectover the course of a 10-second interval;

FIG. 11 is a schematic flowchart of the significant steps in anembodiment of the method of the invention; and

FIG. 12 is a simplified flowchart showing significant steps of a furtherembodiment of the invention.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION

FIG. 1 is a diagram showing a preferred embodiment of the physicalcomponents of the system. The EEG signals are detected by multipleelectrodes 101 from the scalp of a subject 102, where the electrodes arepositioned preferably arranged according to the international 10:20standard system with the addition of mid-point electrodes as necessary.Preferably, the EEG signals are recorded referenced to linked ears using64 scalp electrodes attached to an electrode cap using the nasion as aground. Other techniques for recording the EEG can also be used.

It is preferable that the EEG is analysed as a sequence of overlappingfixed length segments. This technique is further described withreference to FIG. 10. FIG. 10 shows an example of a typical EEG signal201 recorded from a subject over a period of 10 seconds. To illustratethe preferred sampling technique, it is assumed that recorded EEGsignals are digitised and segmented into fixed, overlapping, 2 secondsegments. The first EEG segment 202 extends from 0 to 2 seconds. Thenext EEG segment 203 overlaps with the preceding EEG segment (e.g. from1 to 3 seconds). This process is repeated for all subsequent segments ofthe EEG signal. This example is based on the assumption that the degreeof signal overlap for all EEG segments is 50% of the immediatelypreceding sample. While this only reflects the best segmenting practice,it is possible to segment the EEG signals into any constant timeinterval and with any degree of overlap. The EEG signal segment istypically sampled (i.e. digitised) at anywhere between 200 to 500samples per second.

Referring to FIG. 1, the EEG signal is transmitted as an analog signalvia multiple independent electrical connections 103 that connect eachelectrode 101 to the input ports 104 of an analog filter andamplification device 105. The signals from each electrode, when groupedtogether, constitute the aggregate EEG signal which is then amplifiedand filtered in the analog filter and amplification device 105. Theanalog EEG signal is sent to an analog/digital (“A/D”) converter 106,which digitises the filtered analog EEG signal. Preferably, filtering ofthe digital EEG signal is performed by the analog filter andamplification device 105, which removes any 50 Hz artefacts and othersources of noise that may contaminate subsequent signal analysis.However digital filtering can also be performed by software running onthe central processing unit (“CPU”) of a personal computer (“PC”). Thedigitised EEG signal is sent to a PC 107 via a data connection 108,which includes a serial or parallel connection. Upon entering the PC,the digitised EEG signal is sent to the CPU 109 via internal data busconnections. The CPU 109 controls a memory module 110, which maycomprise of random access memory (“RAM”) components for short-term ortemporary storage and recall of data, or a hard disk or another devicethat provides more permanent storage. The software for processing thedigital EEG signal is also stored in either the RAM or hard disk of thememory module.

The system may process the digitised EEG signal on-the-fly, such that anEEG is repeated obtained over consecutive and constant time intervals,and where each time interval may overlap with the immediately precedingtime interval as described above. The EEG obtained for each timeinterval may be temporarily stored in the RAM memory components of thesystem before it is processed shortly after it has been put in the RAMand removed from the RAM after the EEG for that time interval has beenprocessed. There may be more than one EEG stored in the RAM at any time,which corresponds to the EEGs obtained for different time intervals.

The digitised EEG signal may also be obtained and recorded before it isprocessed. The digitised EEG signal may be recorded on more permanentforms of storage, such as a hard disk, tape drive or a compact disc(“CD”). The recorded EEG can therefore be processed at any time after ithas been recorded or can be used as a reference for comparisons withother EEGs (that may be recorded from the same subject or also fromdifferent subjects) at a future point in time.

Referring to FIG. 1, the CPU 109 runs software to perform ARMA modellingon the digital EEG signal and to calculate the 14 ARMA coefficientsaccording to Equation 15 below. This may be done using the “ARMASAMatlab Toolbox” software by P.M.T Broersen (Delft University ofTechnology), or any of the large number of commercially or freelyavailable ARMA software modelling packages.

Upon determining these 14 coefficients, the CPU 109 uses software, whichmay be the same software package as described above, to calculate andgraphically plot the 8 pole positions on the z-plane for that EEGsegment. The software instructs the CPU 109 to send the graphical datagenerated by the software to a display device 111 controlled by the CPU109, in which the display device 111 may be connected to the CPU 109 viainternal data bus connections. The display device 111 generates a visualrepresentation of the information within the graphical data generated bythe software, which may be in the form of a graph or chart as shown inFIGS. 6, 7 8 and 9.

Although FIG. 1 shows that the system may be implemented with theassistance of additional hardware components, it is possible toimplement some of the features provided by the hardware using software.For example, with reference to FIG. 1, the functions provided by theanalog filter and amplifier 105 and A/D converter 106 can be implementedusing software. As such, it is possible to implement the process offiltering and amplifying an analog EEG signal, A/D conversion(digitising the EEG signal), segmentation of the digitised EEG signal,storage of the digitised EEG signal, solving of the 14 ARMA coefficientsfor each segment of the digitised EEG signal and generating a graphicalplot or other visual representation of a single set or consecutive setsof 8 poles derived from one or multiple segment of the digitised EEGsignal respectively, as one software package.

Before describing the methods of the invention, it is desirable toexplain the theoretical basis of the principles upon which the methodsof the invention are based. The alpha rhythm is arguably the mostobvious recordable feature of the intact human brain. While the exactbasis for its genesis is still controversial it is widely believed thatit arises as a consequence of one or more of the following mechanisms:

-   -   endogenous or exogenous (thalamic) pacing of cortical neurons;    -   oscillatory activity generated through the reciprocal        interactions of excitatory (pyramidal) and inhibitory        (interneuron) cortical neuronal populations; or    -   boundary dependent standing wave generation (Schumann like        resonance) due to long range cortico-cortical connectivity.

However none of these mechanisms are sufficient, either separately ortaken together, in explaining the physiological genesis of the alpharhythm.

A theory of alpha electrorhymogenesis (as discussed in Liley et al.Network: Comput. Neural Syst. 13 (2002) 67-113, the contents of whichare hereby incorporated in this specification) is based upon a detailedspatially continuous two-dimensional mean field theory ofelectrocortical activity. Reference is also made to an article entitledDrug-Induced Modification of System Properties Associated withSpontaneous Human Encephalographic Activity, (Liley D. T. J. et al. PhysRev E 68 (2003) 051906), the contents of which are also incorporatedherein by cross-reference. According to this theory, the brain acts as awhite noise filter to its electrical neural input and the alpha rhythmarises as a result of the filtering of input signals going to thecortex. The filter properties are determined by the bulk(macroscopic/large-scale) anatomical and physiological properties ofexcitatory and inhibitory cortical neurons.

In this theory, inhibition is conceived as having an important role indetermining the properties of the “cortical filter” and thus the spectraof the alpha rhythm generated. In particular the selective modificationof the strength of cortical inhibitory action by benzodiazepines, suchas alprazolam, is associated with specific changes in the properties ofthis filter. As such, it is found that the strength and form of thepopulation inhibitory→inhibitory synaptic interactions are the mostsensitive determinates of the frequency and damping of the emergentalpha band oscillatory activity. Such behaviour arises principallybecause local inhibitory→inhibitory and local inhibitory→excitatory loopdelays that are associated with physiologically andelectroencephalographically plausible alpha activity are longer than thecorresponding local (intra-cortical) and long-range (cortico-cortical)excitatory→excitatory loop delays.

This theory differs from other macroscopic continuum theories in thatthe time course of the unitary inhibitory post-synaptic potential(“IPSP”) is described by a third order differential equation. Lowerorders are theoretically found to be unable to support any appreciableor widespread alpha band activity.

The principal state variables modelled under this theory are the meansoma membrane potentials of local cortical populations of excitatory andinhibitory neurons. The local field potential, and hence the EEG orelectrocorticogram (“ECoG”) signal, is regarded as being linearlyrelated to the mean soma membrane potential of the excitatory neurons.This theory can be cast as a set of coupled non-linear one-dimensionalpartial differential equations that incorporate the major bulkanatomical and physiological features of cortical neurons and includescable delays, neurotransmitter kinetics and cortico-cortical andintra-cortical connectivities. The spontaneous alpha rhythm is theorizedto predominantly arise as a consequence of the local linear propertiesof the cortex. For this reason in the current formulation spatialeffects have been restricted to one dimension.

In accordance with this theory the following non-linear equations(Equations 1, 2, 3 and 4) mathematically represent the brain'selectrical activity, as further described in Liley et al. Network:Comput. Neural Syst. 13 (2002) 67-113: $\begin{matrix}{{\tau\frac{\partial{h\left( {x,t} \right)}}{\partial t}} = {h^{rest} - {h\left( {x,t} \right)} + {{{\overset{\_}{\psi}}_{e}(h)}{I_{e}\left( {x,t} \right)}} + {{{\overset{\_}{\psi}}_{i}(h)}{I_{i}\left( {x,t} \right)}}}} & {{Equation}\quad 1} \\{{\left( {\frac{\partial}{\partial t} + \gamma_{e}} \right)^{2}{I_{e}\left( {x,t} \right)}} = {\Gamma_{e}\gamma_{e}{\exp(1)}\left\{ {{N_{e}^{\beta}{S_{e}\left( h_{e} \right)}} + {\phi\left( {x,t} \right)} + {p_{e}\left( {x,t} \right)}} \right\}}} & {{Equation}\quad 2} \\{{\left( {\frac{\partial}{\partial t} + \gamma_{i}} \right)^{2}{I_{i}\left( {x,t} \right)}} = {\Gamma_{i}\gamma_{i}{\exp(1)}\left\{ {{N_{i}^{\beta}{S_{i}\left( h_{i} \right)}} + {p_{i}\left( {x,t} \right)}} \right\}}} & {{Equation}\quad 3} \\{{{\left( {{I\frac{\partial}{\partial t}} + {\overset{\_}{\upsilon}\Lambda}} \right)^{2}{\phi\left( {x,t} \right)}} - {{\overset{\_}{\upsilon}}^{2}\frac{\partial^{2}{\phi\left( {x,t} \right)}}{\partial x^{2}}}} = {\overset{\_}{\upsilon}\Lambda\quad{N^{\alpha}\left( {{\overset{\_}{\upsilon}\Lambda} + {I\frac{\partial}{\partial t}}} \right)}{S_{e}\left( h_{e} \right)}}} & {{Equation}\quad 4}\end{matrix}$where h=(h_(e),h_(i))^(T), h^(rest)=(h_(e) ^(rest),h_(i) ^(rest))^(T),I_(e)=(I_(ee),I_(ei)), I_(i)=(I_(ie),I_(ii))^(T), N_(ee) ^(B)=(N_(ee)^(B),N_(ei) ^(B))^(T), N_(i) ^(β)=(N_(ie) ^(β),N_(ii) ^(β))^(T),N^(α)=(N_(ee) ^(α),N_(ei) ^(α))^(T), φ=(φ_(e),φ_(i))^(T),Λ=diag(Λ_(ee),Λ_(ei)), τ=diag(τ_(e),τ_(i)),Ψ_(j)(h)=diag(ψ_(j)(h_(e)),ψ_(j)(h_(i))), p_(e)=(p_(ee),p_(ei))^(T),p_(i)=(p_(ie), p_(ii))^(T) and I is the identity matrix, with:S _(j)(h _(j))=S _(j) ^(max)(1+exp[−√{square root over (2)}(h_(j)−{overscore (μ)}_(j))/{circumflex over (σ)}_(j)])⁻¹  Equation 5ψ_(j)(h _(j′))=(h _(j) ^(eq) −h _(j′))/|h _(j) ^(eq) −h _(j′)^(rest)|  Equation 6where j, j′=e, i.

Table 1 is a table which shows the ranges of all the theoreticalparameters (i.e. the numerical values of all anatomical andphysiological parameters) that are used by the above equations togenerate parameter sets that give rise to stable physiological alphaactivity. The ranges in Table 1 refer to the intervals from whichuniform parameter deviates were generated. TABLE 1 Typical parametervalues Typical Symbol Definition Value Range Units e, i Excitatory,inhibitory — — — h_(e), h_(i) Mean soma membrane potential of — — — eand i neurons h_(e) ^(rest), h_(i) ^(rest) Mean resting membranepotential −60, −60 — mV of e and i neurons h_(e) ^(eq), h_(i) ^(eq) Meanreversal potential associated 0, −70 mV with excitation or inhibitionN^(α) _(ee), N^(α) _(ei) Mean total number of connections 4000, 20002000-5000, — that a cell of type e, i receives from 1000-3000 excitatorycells via cortico-cortical fibers N^(β) _(ee), N^(β) _(ei) Mean totalnumber of connections 3034, 3034 2000-5000, — that a cell of type e, ireceives from 2000-5000 excitatory cells via intracortical fibers N^(β)_(ie), N^(β) _(ii) Mean total number of connections 536, 536 — — that acell of type e, i receives from inhibitory cells via intracorticalfibers τ_(e), τ_(i) Effective passive membrane time 0.01, 0.010.005-0.15, s constant 0.005-0.15 κ = Λ_(ee) = Λ_(ei) Characteristicscale of e→e, e→i 0.4 0.1-1.0 cm⁻¹ cortico-cortical fibers ν Meancortico-cortical conduction 700 1-1000 cm s⁻¹ velocity Γ_(e), Γ_(i)Effective excitatory, inhibitory 0.4, 0.8 —, 0.1-2 mV postsynapticpotential peak amplitude γ_(e), γ_(i) Effective excitatory, inhibitory300, 65 100-500, 10-200 s⁻¹ postsynaptic potential rate constant{overscore (μ)}_(e), {overscore (μ)}_(i) Excitatory, inhibitorypopulation −50, −50 −60-0, −60-0 mV thresholds S_(e) ^(max), S_(i)^(max) Excitatory, inhibitory population 100, 100 — Hz mean maximalfiring rates p_(ee), p_(ei) Excitatory input to excitatory, 0, 0 — Hzinhibitory cells p_(ie), p_(ii) Inhibitory input to excitatory, 0, 0 —Hz inhibitory cells {circumflex over (σ)}_(e), {circumflex over (σ)}_(i)Standard deviation for firing 5, 5 — mV threshold in excitatory,inhibitory populations

Non-Linear Equations 1 to 6 need to be transformed into their linearequivalent in order to be solved. To determine theoretically whether thealpha rhythm can be understood in terms of a white noise fluctuationspectrum the above equations are linearized about spatially homogeneoussingular points. For a given set of parameters these singular points canbe obtained by setting all spatial and temporal derivatives to zero andsolving for h_(e). In general these singular points, h_(e)*, aresolutions to the following equation:F(h _(e)(q),q)=0  Equation 7where q represents a vector of model parameters and F(●) is obtainedfrom Equations 1, 2, 3 and 4.

Linearizing Equations 1, 2, 3 and 4 about the spatially homogenoussingular point h_(e)* and transforming to the Fourier domain yields thefollowing equation: $\begin{matrix}{{H_{e}\left( {k,\omega} \right)} = {\frac{{\exp(1)}\Gamma_{e}\gamma_{e}\eta_{e}}{\tau_{e}}\frac{N\left( {k,{\omega\text{:}\quad q}} \right)}{D\left( {k,{\omega\text{:}\quad q}} \right)}{P\left( {k,\omega} \right)}}} & {{Equation}\quad 8} \\{\quad{= {{G_{e}\left( {k,{\omega:\quad q}} \right)}{P\left( {k,w} \right)}}}} & {{Equation}\quad 9}\end{matrix}$where k and ω are wave number and angular frequency respectively.Loosely speaking, k specifies the reciprocal of the characteristicphysical scale over which oscillations of frequency ω occur. H_(e)(k,ω)is the Fourier transform of the mean soma membrane potential ofexcitatory neurons h_(e)(x,t). h_(e)(x,t) has been shown to beproportional to the surface recorded electrical activity, the EEG, ofthe brain. The function G_(e) is the electrocortical transfer function,q is a vector of parameters and P(k,ω)) represents the spatio-temporalform of cortical input.

The terms N(k,ω,q) and D(k,ω,q) in Equation 8 can be expressed as thefollowing Equations 10 and 11, where the corresponding parameters forthe parameter vector ‘q’ in Equation 8 has now been explicitlyidentified in Equations 10 and 11. $\begin{matrix}{{N\left( {k,\omega} \right)} = {\left\{ {{\left( {{\mathbb{i}\omega} + \gamma_{i}} \right)^{2}\left( {{\mathbb{i}\omega} + {\eta_{i}/\tau_{i}}} \right)} - {w_{ii}N_{ii}^{\beta}Q_{i}}} \right\}\left\{ {\left( {\kappa + {{\mathbb{i}\omega}/\upsilon}} \right)^{2} + k^{2}} \right\}}} & {{Equation}\quad 10} \\{{D\left( {k,\omega} \right)} = {\left\{ {{\left( {{\mathbb{i}\omega} + \gamma_{i}} \right)^{2}\left( {{\mathbb{i}\omega} + {\eta_{i}/\tau_{i}}} \right)} - {w_{ii}N_{ii}^{\beta}Q_{i}}} \right\}{\quad{\left\lbrack {{\left\{ {\left( {\kappa + {{\mathbb{i}\omega}/\upsilon}} \right)^{2} + k^{2}} \right\}\left( {{\mathbb{i}\omega} + {\eta_{e}/\tau_{e}}} \right)\left( {{\mathbb{i}\omega} + \gamma_{e}} \right)^{2}} - {w_{ee}{Q_{e}\left( {{N_{ee}^{\alpha}{\kappa\left( {\kappa + {{\mathbb{i}\omega}/\upsilon}} \right)}} + {N_{ee}^{\beta}\left\{ {\left( {\kappa + {{\mathbb{i}\omega}/\upsilon}} \right)^{2} + k^{2}} \right\}}} \right)}}} \right\rbrack - {w_{ei}w_{ie}N_{ie}^{\beta}Q_{e}{Q_{i}\left( {{N_{ei}^{\alpha}{\kappa\left( {\kappa + {{\mathbb{i}\omega}/\upsilon}} \right)}} + {N_{ei}^{\beta}\left\{ {\left( {\kappa + {{\mathbb{i}\omega}/\upsilon}} \right)^{2} + k^{2}} \right\}}} \right)}}}}}} & {{Equation}\quad 11} \\{w_{j^{\prime}j} = {{\exp(1)}\Gamma_{j^{\prime}}\gamma_{j^{\prime}}\eta_{j^{\prime}}{{\psi_{j^{\prime}}\left( h_{j}^{*} \right)}/\left( {\tau_{j^{\prime}}\eta_{j}} \right)}}} & {{Equation}\quad 12} \\{\eta_{j} = {1 + {{\exp(1)}{\Gamma_{e}\left( {N_{ej}^{\alpha} + N_{ej}^{\beta}} \right)}{{S_{e}\left( h_{e}^{*} \right)}/\left( {\gamma_{e}{{h_{e}^{eq} - h_{j}^{rest}}}} \right)}} + {{\exp(1)}\Gamma_{i}N_{ij}^{\beta}{{S_{i}\left( h_{i}^{*} \right)}/\left( {\gamma_{i}{{h_{i}^{eq} - h_{j}^{rest}}}} \right)}}}} & {{Equation}\quad 13} \\{Q_{j} = \left. {{\partial S_{j}}/{\partial h_{j}}} \right|_{h_{j} = h_{j}^{*}}} & {{Equation}\quad 14}\end{matrix}$

From Equation 10, the highest order in ω is 5, which corresponds to themoving average order of the ARMA model. From Equation 11, the highestorder in ω is 8, which corresponds to the auto-regressive order of theARMA model.

Equations 8, 10 and 11 can be rewritten in a summary form as Equations12, 13 and 14, as shown above.

Equation 14 can be rewritten as a difference equation, as shown inEquation 15, which represents a linear time invariant discrete timesystem: $\begin{matrix}{{y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}} & {{Equation}\quad 15}\end{matrix}$where y[n] is the digitised EEG signal, u[n] is a Gaussian white noiseprocess and a_(k) and b_(k) are coefficients to be determined for agiven EEG time series.

Equation 15 represents an (8,5) order ARMA model, where the specificvalues of the orders are derived from Equations 10 and 11. The 14coefficients from the ARMA model can be determined using any of thelarge number of commercially or freely available ARMA software modellingpackages, such as the ARMASA Matlab Toolbox software by P.M.T Broersen(Delft University of Technology).

To understand how the 14 coefficients so obtained can be used to measurebrain function, Equation 15 is rewritten in the z-domain by taking thez-transform. Thus Equation 15 can be equivalently written in thez-domain as: $\begin{matrix}{{Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}} & {{Equation}\quad 16}\end{matrix}$

Solutions to A(z)=0 in Equation 16 will give the system poles andsolutions to B(z)=0 in Equation 16 will give the system zeros. Ingeneral, these solutions are complex with |z|<1. The maximum power ofthe denominator in Equation 16 suggests that there are 8 unique systempoles. The eight complex solutions to A(z)=0 are then plotted on thez-plane.

The location of the eight poles derived from Equation 16 represent thestate of the brain as determined by the EEG signals recorded over theparticular time interval. With reference to FIG. 2, the set of eightpoles from one EEG segment 20 is plotted on the z-plane 21. Withreference to FIG. 3, the application of Equation 15 to subsequentsegments of EEG from the entire EEG sample allows further sets of eightpoles 31 to be determined and plotted onto the same z-plane 30 thatcontains the poles plotted from the preceding EEG samples 31.

Theoretically, the results in FIG. 3 can be interpreted with referenceto FIG. 4. FIG. 4 is the schematic representation of the predictedeffects of increasing the strength of neuronal populationinhibitory→inhibitory and inhibitory→excitatory synaptic interactions.The filled circle 40 approximately represents the theoretical loci ofthe dominant poles associated with electroencephalographically plausibleeyes-closed alpha activity. In other words, the filled circle 40represents the most weakly damped pole, which can be thought of ascorresponding to the most dominant oscillatory component making up thehuman alpha rhythm. For any recording of human alpha rhythm, a frequencyanalysis using a Fourier transform would reveal the approximatefrequency of this dominant pole or the dominant oscillatory component.The arrows 41 and 42 in FIG. 4 indicate the mean predicted direction ofthe motion of these poles in response to increases ininhibitory→inhibitory$\overset{\_}{\left( {{\partial\omega^{*}}/{\partial{\hat{N}}_{ii}^{\beta}}} \right)}$41 and inhibitory→excitatory$\overset{\_}{\left( {{\partial\omega^{*}}/{\partial{\hat{N}}_{ie}^{\beta}}} \right)}$42 synaptic strength.

FIG. 5 shows the same information as FIG. 4 as plotted on the s-plane(Laplace or Fourier plane) rather than the z-plane. The filled circle 50approximately represents the theoretical loci of the dominant polesassociated with electroencephalographically plausible eyes-closed alphaactivity. The arrows 51 and 52 in FIG. 5 indicate the mean predicteddirection of the motion of these poles in response to increases ininhibitory→inhibitory$\overset{\_}{\left( {{\partial\omega^{*}}/{\partial{\hat{N}}_{ii}^{\beta}}} \right)}$51 and inhibitory→excitatory$\overset{\_}{\left( {{\partial\omega^{*}}/{\partial{\hat{N}}_{ie}^{\beta}}} \right)}$52 synaptic strength.

The decay rate is related to the sharpness of the resonance of thedominant oscillatory component in the recorded EEG signal. Increasingdecay rates would correspond to the broadening of the alpha resonance inhuman EEG recordings. In FIG. 5, the arrow 51 represents an increasingdecay rate as it moves away from the filled circle 50, which representsa single pole. The arrow 52 represents a decreasing decay rate as itmoves away from the pole 50. In FIG. 4, the closer that the pole 40moves to the boundary of the unit circle 43 the smaller the decay,whereas the further the pole moves from the boundary 43 the larger thedecay. Referring to FIG. 4, an anti-clockwise motion of the pole 40implies that the pole's frequency increases, whereas a clockwise motionof the pole implies that the frequency decreases. Thus, according tothis theory of alpha rhythm generation, changes in the decay rate(s)associated with the dominant oscillatory component gives information inaddition to that which can be obtained using the Fourier analysis ofhuman EEG.

FIGS. 6 and 7 show the position of the poles and zeros in a pole-zeroplot for a typical subject before (as shown by the “−BZ” poles andzeros) and after (as shown by the “+BZ” poles and zeros) theadministration of the benzodiazepine as an oral dose of alprazolam. Asimilar pole-zero plot for a typical subject is shown in FIGS. 8 and 9before (as shown by the “−PL” poles and zeros) and after (as shown bythe “+PL” poles and zeros) the administration of a placebo. Where theyapply in FIGS. 6, 7, 8 and 9, poles are indicated with “+” or “*” andzeros indicated with “◯” or “□”.

FIGS. 7 and 9 show in more detail the region of the z-plane, from FIGS.6 and 8 respectively, corresponding to a region of 8-13 Hz activity. Theimportant features to note are:

-   -   (i) the distinct groupings of poles and zeros populating the        z-plane;    -   (ii) distinct populations of poles having frequencies lying in        the range 8-13 Hz;    -   (iii) clear differences between the location of the centroids of        the alpha poles before (as indicated by the “−BZ” poles and        zeros in FIGS. 6 and 7) and following (as indicated by the “+BZ”        poles and zeros in FIGS. 6 and 7) administration of the        benzodiazepine; and    -   (iv) insubstantial differences between the location of the alpha        poles before (as indicated by the “−PL” poles and zeros in FIGS.        8 and 9) and following (as indicated by the “+PL” poles and        zeros in FIGS. 8 and 9) administration of the placebo.

It is evident from FIG. 7 that the variability of the alpha polelocation after the ingestion of the benzodiazepine is more pronouncedthat in the other three conditions. Compared to the placebo condition,as shown in FIG. 9, it can be seen that alprazolam causes a significantshift in the most weakly damped pole constituting the alpha rhythm, suchthat its corresponding frequency and damping both increased. In theabsence of any other poles this implies that alprazolam causes the alphaspectrum to shift to the right and broaden, as shown in FIGS. 7 and 9.Variations in the mean location of these clusters of poles and theirdistribution will result as a consequence of ongoing normal behaviour,disease progression and state, or pharmacological or therapeuticinterventions or manipulations. As such, the mean location of the polesis a measure of brain state and the movement of the mean location ofthese poles is a measure of changes in brain state or function.

FIG. 11 is a flowchart 119 which diagrammatically illustrates some ofthe important steps in the method described above. Briefly, step 120represents obtaining EEG signals from the brain of the subject. Step 122represents digitisation as carried out by the converter 106. Step 124represents digital filtering which is carried out in the PC 107. Step126 represents segmentation of the EEG signal which is also carried outin the PC 107. Step 128 represents computation carried out by the CPU109 in order to obtain the coefficients A₁-A₈ and B₀-B₅. Step 130represents the step of solving the z-domain polynomial equation in orderto obtain system poles and step 132 represents plotting the system polesin the z-plane. These poles can be displayed on the display device 111.Steps 128, 130 and 132 are repeated for each of the frames.

Step 134 represents the step of assessment of the results by referenceto the distribution of clusters of poles in the z-plane. This step wouldnormally be carried out by an operator.

FIG. 12 shows a flowchart 140 which shows some of the important steps ofembodiments of methods of the invention. The flowchart 140 includes astep 142 which is regarded as an initial assessment of the brain stateof a subject. The step 142 may comprise all of the steps 120 to 134 ofthe flowchart 119. In other words the operator would carry out aninitial assessment of the subject prior to carrying out of an event, asindicated by step 114. The event 114 may be the administration of acognitively active pharmaceutical agent to a subject being tested or theadministration of an anaesthetic to the patient. Step 146 representscontinuation of the monitoring of the results after the event 146 so asto determine the effect of the event. The continued assessment step 146typically includes all of the steps 120 to 134 of the flowchart 119 ofFIG. 11. For instance where the event is the administration of a dose ofa cognitively active pharmaceutical agent, the step 146 enablesassessment of the effect which the agent has on the brain of thesubject. This assessment is, of course, objective rather thansubjective, in accordance with the principles of the invention. Wherethe step 144 is the administration of an anaesthetic to the patient, thestep 146 enables the continued monitoring of the clusters of poles bythe anaesthetist or an operator in order to monitor the state ofanaesthetic depth of the patient so that the anaesthetist is able tocontrol the rate of application of anaesthetic to the subject. Again, inaccordance with the principles of the invention, this assessment is doneobjectively rather than subjectively.

The reference to any prior art in this specification is not and shouldnot be taken as an acknowledgement or any form of suggestion that priorart forms part of the common general knowledge in Australia.

Many modifications will be apparent to those skilled in the art withoutdeparting from the spirit and scope of the invention.

1. A method for assessing brain state by analysing mammalian brainelectroencephalogram (EEG) recordings using an eighth orderautoregressive and fifth order moving average discrete time equation. 2.A method as claimed in claim 1, further including the steps of: taking az-transform for said eighth order autoregressive and fifth order movingaverage discrete time equation to obtain a z-domain equation,determining poles and zeroes in the solution of the z-domain equation;and plotting the poles onto the complex plane.
 3. A method of assessingthe state of a mammalian brain including the steps of: (i) obtaining anelectroencephalogram (EEG) from the brain; (ii) digitising the EEG todefine a digitised EEG data signal; (iii) segmenting the EEG data signalinto time frames of fixed length, y[n]; (iv) approximating eachdigitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; and (xi) assessing the state ofthe brain by reference to the position and distribution of at least someof said clusters of poles as mapped in the complex plane.
 4. A method ofassessing the state of a mammalian brain including the steps of: (i)obtaining an electroencephalogram (EEG) from the brain; (ii) digitisingthe EEG to define a digitised EEG data signal; (iii) segmenting the EEGdata signal into time frames of fixed length, y[n]; (iv) approximatingeach digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; and (xi) administering anintervention to the brain; (xii) repeating steps (i) to (x) at leastonce; (xiii) monitoring movement of at least some of said clusters ofpoles in the complex plane; and (xiv) assessing the state of the brainby reference to movement of at least some of said clusters of poles asmapped in the complex plane.
 5. A method as claimed in claim 3 includingthe step of filtering the EEG to remove noise signals therefrom prior tocarrying out step (iii).
 6. A method as claimed in claim 3, wherein saidEEG is obtained and recorded before it is processed.
 7. A method ofassessing the state of a mammalian brain including the steps of: (i)obtaining a first electroencephalogram (EEG) from the brain; (ii)digitising the EEG to define a digitised EEG data signal; (iii)segmenting the EEG data signal into time frames of fixed length, y[n];(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; (xi) obtaining a second EEG fromsaid brain at a later time; (xii) repeating steps (ii) to (x) inrelation to the second EEG at least once; (xiii) monitoring the movementof at least some corresponding clusters of poles in the complex planederived from the first and second EEGs respectively; and (xiv) assessingthe state of the brain by reference to movement of at least some of saidclusters of poles as mapped in the complex plane.
 8. A method as claimedin claim 6 including the step of filtering the EEG to remove noisesignals therefrom prior to carrying out step (iii).
 9. A method asclaimed in claim 7, wherein said first and second EEG is obtained andrecorded before it is processed.
 10. A method as claimed in claim 7,wherein said EEG, or said first and second EEG, is obtained and recordedin its entirety for processing at a later point in time.
 11. A method asclaimed in claim 7, wherein said EEG, or said first and second EEG, iseach repeatedly obtained over consecutive and constant time intervals.12. A method as claimed in claim 11, wherein a said time interval mayoverlap with an immediately preceding time interval.
 13. A method asclaimed in claim 3, wherein the step of step (x) is repeatedcontinuously to track the motion of the poles from each segment.
 14. Amethod as claimed in claim 3, wherein the step of step (xi) includes thesteps: (xi)(a) taking the centroid of the poles for each cluster ofpoles; and (xi)(b) monitoring and comparing the movement of saidcentroids.
 15. A method as claimed in claim 14 including the step of:(xi)(c) analysing the statistical variability of the poles in saidclusters of poles.
 16. A method as claimed in claim 7, wherein the stepof step (xiv) includes the steps of: (xiv)(a) taking the centroid of thepoles for each cluster of poles; and (xiv)(b) monitoring and comparingthe movement of said centroids.
 17. A method as claimed in claim 16including the step of: (xiv)(c) analysing the statistical variability ofthe poles in said clusters of poles.
 18. A method of assessing theefficacy of a cognitively active pharmaceutical agent including thesteps of: (i) obtaining a first electroencephalogram (EEG) from thebrain of a subject; (ii) digitising the EEG to define a digitised EEGdata signal; (iii) segmenting the EEG data signal into time frames offixed length, y[n]; (iv) approximating each digitised time frame by afirst equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; (xi) administering a dose of acognitively active pharmaceutical agent to the subject; (xii) obtaininga second EEG from said brain after step (xi); (xiii) repeating steps(ii) to (x) in relation to the second EEG at least once; (xiv)monitoring the movement of at least some corresponding clusters of polesin the complex plane derived from the first and second EEGsrespectively; and (xv) assessing the efficacy of the cognitively activepharmaceutical agent by reference to movement of at least some of saidclusters of poles as mapped in the complex plane.
 19. A method ofassessing the state of vigilance or alertness of a subject including thesteps of: (i) obtaining an electroencephalogram (EEG) from the brain ofa subject; (ii) digitising the EEG to define a digitised EEG datasignal; (iii) segmenting the EEG data signal into time frames of fixedlength, y[n]; (iv) approximating each digitised time frame by a firstequation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; (xi) repeating steps (i) to (x);(xii) monitoring movement of at least some of said clusters of poles inthe complex plane; and (xiii) assessing the state of vigilance oralertness of the subject by reference to movement of at least some ofsaid clusters of poles as mapped in the complex plane.
 20. A method ofassessing the state of sleep of a subject including the steps of: (i)obtaining an electroencephalogram (EEG) from the brain of a subject;(ii) digitising the EEG to define a digitised EEG data signal; (iii)segmenting the EEG data signal into time frames of fixed length, y[n];(iv) approximating each digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; (xi) repeating steps (i) to (x);(xii) monitoring movement of at least some of said clusters of poles inthe complex plane; and (xiii) assessing the state of sleep of thesubject by reference to movement of at least some of said clusters ofpoles as mapped in the complex plane.
 21. A method of assessing thestate of anaesthesia of a subject including the steps of: (i) obtainingan electroencephalogram (EEG) from the brain of a subject whileanaesthetised; (ii) digitising the EEG to define a digitised EEG datasignal; (iii) segmenting the EEG data signal into time frames of fixedlength, y[n]; (iv) approximating each digitised time frame by a firstequation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; (xi) repeating steps (i) to (x);(xii) monitoring movement of at least some of said clusters of poles inthe complex plane; and (xiii) assessing the state of anaesthesia of thesubject by reference to movement of at least some of said clusters ofpoles as mapped in the complex plane.
 22. A method of assessing thestate of anaesthesia of a subject including the steps of: (i) obtaininga first electroencephalogram (EEG) from the brain; (ii) digitising theEEG to define a digitised EEG data signal; (iii) segmenting the EEG datasignal into time frames of fixed length, y[n]; (iv) approximating eachdigitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(v) solving the first equation to determine coefficients a₁ to a₈ and b₀to b₅; (vi) performing a z-transform on the first equation to obtain asecond, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(vii) substituting each of the values of the coefficients into thez-domain equation; (viii) solving A(z)=0 for z in the second equation todetermine the poles; (ix) plotting the poles in the complex plane; (x)repeating steps (iv) to (ix) for each frame in the sample to determineclusters of poles in the complex plane; (xi) administering theanaesthetic to the patient; (xii) obtaining a second EEG from said brainafter step (xi); (xiii) repeating steps (ii) to (x) in relation to thesecond EEG at least once; (xiv) monitoring the movement of at least somecorresponding clusters of poles in the complex plane derived from thefirst and second EEGs respectively; and (xv) assessing the state ofanaesthesia of the subject by reference to movement of at least some ofsaid clusters of poles as mapped in the complex plane.
 23. A systemhaving means for assessing brain state by analysing mammalian brainelectroencephalographic recordings using an eighth order autoregressiveand fifth order moving average discrete time model equation.
 24. Asystem having means for performing the method as claimed in claim
 1. 25.Apparatus for assessing brain state of a subject, the apparatusincluding a plurality of electrodes for picking up EEG signals from thebrain of the subject; digitising means for converting the EEG signals toa digitised EEG data signal; computing means for: (i) segmenting the EEGdata signal into time frames of fixed length, y[n]; (ii) approximatingeach digitised time frame by a first equation:${y\lbrack n\rbrack} = {{- {\sum\limits_{k = 1}^{8}{a_{k}{y\left\lbrack {n - k} \right\rbrack}}}} + {\sum\limits_{k = 0}^{5}{b_{k}{u\left\lbrack {n - k} \right\rbrack}}}}$(iii) solving the first equation to determine coefficients a₁ to a₈ andb₀ to b₅; (iv) performing a z-transform on the first equation to obtaina second, z-domain equation:${Y(z)} = {{\frac{\sum\limits_{k = 0}^{5}{b_{k}z^{- k}}}{1 + {\sum\limits_{k = 1}^{8}{a_{k}z^{- k}}}}{U(z)}} = {\frac{B(z)}{A(z)}{U(z)}}}$(v) substituting each of the values of the coefficients into thez-domain equation; (vi) solving A(z)=0 for z in the second equation todetermine the poles; (vii) plotting the poles in the complex plane; anddisplay means for displaying the poles, to thereby enable assessment ofthe brain state of the subject by reference to the position anddistribution of clusters of said poles.
 26. A computer readable mediumhaving computer program instructions stored thereon which, when executedby a computer, performs the steps in the methods as claimed in claim 3.